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Abstract (eng):

Multi-stage stochastic programs (MSP) pose some of the more challenging optimization
problems. Because such models can become rather intractable in general, it is important to
design algorithms that can provide approximations which, in the long run, yield solutions that are
arbitrarily close to an optimum. In this paper, we propose a statistically motivated sequential
sampling method that is applicable to multi-stage stochastic linear programs, and we refer to it as
the multistage stochastic decomposition (MSD) algorithm. As with earlier SD methods for two-
stage stochastic linear programs, this approach preserves one of the most attractive features of
SD: asymptotic convergence of the solutions can be proven (with probability one) without any
iteration requiring more than a small sample-size. This data-driven approach also allows us to
sequentially update value function approximations, and the computations themselves can be
organized in a manner that decomposes the scenario generation (stochastic) process from the
optimization computations. As a by-product of this study, we also show that SD algorithms are
essentially approximate dynamic programming algorithms for SP. Our asymptotic analysis also
reveals conceptual connections between multiple SP algorithms.

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